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Transactions of the American Mathematical Society

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Isocategorical groups and their Weil representations

Author: César Galindo
Journal: Trans. Amer. Math. Soc. 369 (2017), 7935-7960
MSC (2010): Primary 16W30, 20C05
Published electronically: May 1, 2017
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Abstract: Two groups are called isocategorical over a field $ k$ if their respective categories of $ k$-linear representations are monoidally equivalent. We classify isocategorical groups over arbitrary fields, extending the earlier classification of Etingof-Gelaki and Davydov for algebraically closed fields. In order to construct concrete examples of isocategorical groups a new variant of the Weil representation associated to isocategorical groups is defined. We construct examples of non-isomorphic isocategorical groups over any field of characteristic different from two and rational Weil representations associated to symplectic spaces over finite fields of characteristic two.

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Additional Information

César Galindo
Affiliation: Departamento de Matemáticas, Universidad de los Andes, 18 A 12 Bogotá, Colombia

Keywords: Hopf-Galois objects, tensor categories, isocategorical groups, Weil representations.
Received by editor(s): June 15, 2015
Received by editor(s) in revised form: December 11, 2015
Published electronically: May 1, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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